Descrição:
A graph parameter is self-dual in some class of graphs embeddable in some surface if its value does not change in the dual graph by more than a constant factor. Self-duality has been examined for several width parameters, such as branchwidth, pathwidth, and treewidth. In this paper, we give a direct proof of the self-duality of branchwidth in graphs embedded in some surface. In this direction, we prove that bw ( G ∗ ) ≤ 6 ⋅ bw ( G ) + 2 g − 4 for any graph G embedded in a surface of Euler genus g . Highlights ► A graph parameter is self-dual in a class of graphs embeddable in a surface if its value does not change in the dual graph by more than a constant factor. ► Self-duality has been examined for several width parameters, such as branchwidth, pathwidth, and treewidth. ► In this paper, we give a direct proof of the self-duality of branchwidth in graphs embedded in some surface. ► Namely, we prove that bw ( G ∗ ) ≤ 6 ⋅ bw ( G ) + 2 g − 4 for any graph G embedded in a surface of Euler genus g .